# Average

## What is Meant by Average or Definition of Average?

• The
mean value which is equal to the ratio of the sum of the number of a
given set of values to the total number of values present in the set
is known as average.

• Average
has many applications both in real-life.

•  Suppose
if we need to find the average age of men or women in a village or
average female height in India, then we can calculate it by adding
all the values and dividing it by the number of values we have

• Here’s
the average formula in maths that evaluates the average of the given
set of numbers:

Average
formula in maths  = $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

### Average Symbol:

• The
average can basically be defined as the mean of the values which are
represented by x̄ (x bar) also known as the average
symbol.

• The
average symbol can be denoted by ‘μ’.

### Average Formula in Maths:

The
formula that will tell you how to calculate the average of a list of numbers
or values is very simple in Mathematics.

Here
are the steps that will tell you how to calculate the average:

Step
1)

Firstly, you need to add all the numbers given in the list

Step
2)

Then divide the calculated sum by the number of terms given in the
list.

Step
3)

The average of numbers can be expressed as:

Average
= Sum of Values of the list/ Total Number of values in the list

Here’s
an average example for better understanding,

Given
a set of values: 1, 2, 3, 4, and 5.

We
know that Average = Sum of all the values of the list / total number of
values in the list.

Step
1)
Sum
of the numbers (1+2+3+4+5) = 15

Step
2)
Total
number of terms = 5, divide the sum by the total number of terms,

Putting
the sum and the number of terms in the formula that we know from the
definition of average,

Average
= Sum of Values of the list/ Total Number of values in a list

Average
= 15/5 = 3

### What is the Average of Negative Numbers?

If
there are negative numbers present in the list of numbers, even then the
process or formula to calculate the average remains the same.

Average
of negative numbers =  $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Let’s
understand the concept of an average of negative numbers with an
example:

Average
examples: Find the average of 4, −7, 5, 10, −1.

Solution)
Lets’ first find the sum of the given numbers,

=
4 + (-7) + 5 + 10 + (-1)

=
4– 7 + 5 + 10 – 1

=
11

Total
number of terms = 5

As
we know the formula to calculate the average from the definition of
average,

Average
= $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Average
= $\frac{6}{5}$

Average
is equal to 1.2.

### What is the Difference Between Mean and Average?

Here’s
the main difference between mean and average,

## Difference Between Mean and Average

 Average can be defined as the sum of values divided by the total number of terms. Whereas, mean can be defined as the sum of the largest and the smallest number in the list divided by 2.

### Questions to Be Solved (Average Examples):

Question
1)

Find the average of the first five even numbers.

Solution)
In Mathematics, the first five even numbers are as follows: 2, 4, 6, 8,
10

Now
we will add these numbers = 2 + 4 + 6 + 8 + 10 = 30

Total
number of terms = 5

As
we know the formula to calculate the average,

Average
= $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Average
= $\frac{30}{5}$

The
average is equal to 6.

Question
2)

Find the average of the given numbers 6, 13, 17, 21, 23.

Solution)
Let’s add the given numbers =

=
6 + 13 + 17 + 21 + 23 is equal to 80

Total
number of terms = 5

As
we know the formula to calculate the average,

Average
= $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Average
= $\frac{80}{5}$

The
average is equal to 16.

Question
3)

If the age of 10 students in a football team is 12, 13, 11, 12, 13, 12, 11,
12, 12, 2. Then find the average age of the students in the football
team.

Solution)
Given,
the age of students are 12, 13, 11, 12, 13, 12, 11, 12, 12 , 2.

Let’s
find the sum of the ages of students,

Sum
= (12+13+11+12+13+12+11+12+12+2) = 120

Total
number of terms = 10

As
we know the formula to calculate the average,

Average
= $\frac{ Sum \; of \; the \; age \; of \; the \; students \; of \; the \; football \; team }{ Total \; number \; of \; students}$

Average
= $\frac{120}{10}$

The
average age of the students of the football team is equal to 12.

Question
4)

If the heights of females in a class are 5.5, 5.3, 5.7, 4.9, 6, 5.1, 5.8,
5.6, 5.4, and  6. Then find the average height of females of the
class.

(Image

Solution)
Given the height of females= 5.5, 5.3, 5.7, 5.9, 6, 5.1, 5.8, 5.6, 5.4,
6

Sum
= (5.5+5.3+5.7+4.9+6+5.1+5.8+5.6+5.4+6)

Total
number of terms = 10

As
we know the formula to calculate the average,

Average
= $\frac{ Sum \; of \; the \; heights \; of \; females }{ Total \; number \; of \; females}$

Average
= $\frac{55.3}{10}$

The
average height of the females in the class is 5.3.

1.
How Do I Calculate the Average and Why is Average
Important?

The average of
a set of numbers can be calculated by finding the sum of
the numbers divided by the total number of values (n) in
the set. For example, suppose we want to find
the average of 1, 5, 4, 7, and 13. We simply
find the sum of the numbers: 1+5+4+7+13 = 30 and as
there are five numbers, when we divide 30 by 5 to get 6.
Average can be easily calculated using the average
calculator.

Average
is important because –

1.
Average helps us to summarize a large amount of data
into a single value.

2.
Average indicates some variability around any single
value within the original data.

2.
Why Do We Calculate the Average and What Do You Mean
By Average?

The
term average is generally used frequently in
everyday life to express an amount
that is typical for a group of people or a
group of things. Averages are useful because
they:

• They
summarize a large amount of data into a single
value.

• Average
indicates that there is some
variability around this single value within the
original data.

Average
can be easily calculated using the average
calculator.

We
can easily calculate the average using the average
calculator. The result that we get when we add two
or more numbers together and divide the sum by the total
number of terms is known as average. Average example,
suppose if we want to find the average of 1,
6, 3, and 2. We simply find the sum of the numbers:
1+6+3+2= 12 and as there are four numbers (n=4), when we
divide 12 by 4 we get 3.